Question

Alexa compares the domain and range of the functions ​f(x)equalsStartRoot x EndRoot and ​g(x)equals2 Superscript x. What is​ Alexa's error?
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Part 1
The domain of​ f(x) is
  
enter your response here and the domain of​ g(x) is
  
enter your response here. The range of​ f(x) is
  
enter your response here and the range of​ g(x) is
  
enter your response here. ​So, Alexa is incorrect because
▼
the ranges are different.
the domains are different.
both the domain and the range are different.
​(Type your answers in interval​ notation.)

Answer 1

The domain of f(x) is [0, ∞) and the domain of g(x) is (-∞, ∞).
The range of f(x) is [0, ∞) and the range of g(x) is (0, ∞).
So, Alexa is incorrect because both the domain and the range are different.

Explanation: sqrt(x) is defined only for x ≥ 0, while 2^x is defined for all real x; sqrt(x) can equal 0 but 2^x is always positive (never 0).